On multiple sites including at least en.wiktionary.org and en.wikipedia.org, it is impossible to search for a word which has diacritics by entering the word without diacritics, and vice versa, e.g. the searches
https://en.wiktionary.org/w/index.php?search=ἔθανον
https://en.wiktionary.org/w/index.php?search=ἐθάνετον
will fail, while
https://en.wiktionary.org/w/index.php?search=ἔθᾰνον
https://en.wiktionary.org/w/index.php?search=ἐθᾰ́νετον.
will succeed. However, the latter case requires not only knowledge of the length of the vowel (which the user may very well be trying to find) but also the ability to type it on the keyboard.
(The corresponding problem also exists—e.g. one cannot find κλίνω by searching for κλῑ́νω. Ideally the page κλίνω should include length information, but not all entries have yet been thusly updated.)
Note that this problem exists both for precomposed diacritics (ἔθᾰνον) and also combining diacritics (ἐθᾰ́νετον—ᾰ́ = U+1FB0 U+0301.)
Additionally, typing e.g. αθανατος into the search bar does not bring up ἀθάνατος. This is, from the user's eyes, a regression. Previously—and I don't know whether this is the fault of Cirrus or not—it was possible to do this. And this is a desirable if not necessary ability—it is often difficult to read diacritics (try distinguishing ἀ from ἁ in some fonts/handwriting), and if you study original inscriptions or papyri, no diacritics well be given at all.
This problem is not limited to the Greek script. Bugs have been filed to this effect for Cyrillic (T124592 and T102298), Hebrew (T71361), Devanagari and Arabic (T29055), as well as Latin (T123179 and T104814).
(Note that in the case of Latin the problem is only partial: searching for any one of 'Bronte' (no diacritic), 'Brónte' (precomposed character), or 'Brónte' (combining diacritic) will yield the expected pages Brontë and Bronte both in the suggestion box and the results page, however, searching for 'Bro̍nte' (combining diacritic) will yield Brontë and Bronte in the suggestion box but not in the results page. Additionally, the list of pages in the suggestion box is much shorter and only apparently includes pages whose titles match exactly up to the point of the diacritic—so while Brónte matches pages beginning with bry-, Bro̍nte doesn't. The reason for this discrepancy between Brónte and Bro̍nte is apparently that o̍ does not have a canonically equivalent precomposed form. This is supported by the fact that a search for Bront́e fails just as Bro̍nte does.)
[EDIT: I changed the example above, κλī́νω, to κλῑ́νω. The first one uses a Latin i with a macron (ī), while the second one uses a Greek iota with a macron (ῑ)—the visual difference is in the tail at the bottom of the character. Both have an additional combining acute accent attached. I agree that distinguishing ἀ and ἁ in handwriting and some fonts is almost impossible, but it seems fair to assume the ı/ι-shaped thing in the middle of a Greek word is an iota, right? —TJones]